# Number System - Natural Numbers (cardinal and ordinal numbers) - $\mathbb{N}$

A natural number $\mathbb{N}$ can be used for two purposes:

• to count (ie describe the size of a set)
• to order (ie or to describe the position of an element in a sequence).
0, 1, 2, 3, 4, ... or 1, 2, 3, 4,

The natural numbers are those used for:

Operation Example Words
counting there are six coins on the table cardinal numbers
ordering this is the third largest city in the country ordinal numbers

## 3 - Number systems

N is a number system.

where:

## 4 - Representation

### 4.1 - Symbol

In the base 10 numeral system, the symbols for natural numbers are written using ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

### 4.2 - Class

In set theory, natural numbers can be represented by classes of equivalent sets. For instance, the number 3 can be represented as the class of all sets that have exactly three elements.